perplexus.info :: Just Math : Super Exponentiation Surmise

Super Exponentiation Surmise (Posted on 2022-07-31)

Find all real values x that satisfy this equation:
x^{x^x} = (1/2)^√2

Provide adequate reasoning for your answer.

Note: a^b^c is equal to a^(b^c)《rather than (a^b)^c》

See The Solution Submitted by K Sengupta

Rating: 4.5000 (2 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)

or graphically

| Comment 2 of 13 |

Or using Desmos to plot y = x^(x^x) and y = (1/2)^sqrt(2) shows an intersection at x = 1/4.

And, incidently, interpreting incorrectly as (a^b)^c yield no solution.

But so far, an analytical solution escapes me.

Posted by Larry on 2022-07-31 09:39:51

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